Solve for $x$ and $y$ using elimination. ${-3x-3y = -36}$ ${4x+3y = 40}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-3x-3y = -36}\thinspace$ to find $y$ ${-3}{(4)}{ - 3y = -36}$ $-12-3y = -36$ $-12{+12} - 3y = -36{+12}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 4}$ into $\thinspace {4x+3y = 40}\thinspace$ and get the same answer for $y$ : ${4}{(4)}{ + 3y = 40}$ ${y = 8}$